How do I put a texture on top of a normal map?
This is how you would do it in Cycles:

After adding both images in Image Texture nodes.
Plug your color map into the Color socket of a Diffuse BSDF shader node.
Take the normal map Image Texture, make sure to set it to "Non-Color Data" and plug it in to the Color socket of a Normal Map node. Then, link normal map to the Normal socket of the same Diffuse BSDF that the color map was linked to earlier.